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Search: id:A007323
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| A007323 |
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Number of bases for symmetric functions of n variables; also number of semigroups of genus n.
(Formerly M1064)
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+0
1
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| 1, 2, 4, 7, 12, 23, 39, 67, 118, 204, 343, 592, 1001, 1693, 2857, 4806, 8045, 13467, 22464, 37396, 62194, 103246, 170963, 282828, 467224, 770832, 1270267, 2091030, 3437839, 5646773, 9266788, 15195070, 24896206, 40761087, 66687201, 109032500, 178158289
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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a(1)-a(16) computed by Shizuo Kakutani.
D. Zagier, personal communication.
M. Bras-Amoros, Fibonacci-Like Behavior of the Number of Numerical Semigroups of a Given Genus, Semigroup Forum, 2007.
M. Bras-Amoros and A. de Mier, Representation of Numerical Semigroups by Dyck Paths, Semigroup Forum.
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LINKS
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Maria Bras-Amoros, Table of n, a(n) for n = 1..50
Maria Bras-Amoros, Title?
Nivaldo Medeiros, Numerical Semigroups
Index entries for sequences related to semigroups
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FORMULA
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Comments from Maria Bras-Amoros (maria.bras@gmail.com), Oct 24 2007: Conjectures: A) a(n) >=a(n-1)+a(n-2); B) a(n)/(a(n-1)+a(n-2)) approaches 1; C) a(n-1)/a(n) approaches the golden ratio.
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EXAMPLE
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a(1)=1 because the unique numerical semigroup with genus 1 is N \ {1}
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CROSSREFS
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Adjacent sequences: A007320 A007321 A007322 this_sequence A007324 A007325 A007326
Sequence in context: A072641 A135360 A082548 this_sequence A099604 A026790 A054165
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KEYWORD
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nonn,nice
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AUTHOR
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njas, Don Zagier, Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
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More terms from Maria Bras-Amoros (maria.bras@gmail.com), Oct 24 2007. Computations were done with the help of Jordi Funollet and Josep M. Mondelo.
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